Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area Blue.
The radius of the inscribed small circle is 2 units.
a = 2atan(⅓)°
b = 2atan(⅕)°
c = 180-a-b
c = (180-2atan(⅓)-2atan(⅕))°
sin(2atan(⅓)) = d/16
d = (48/5) units.
cos(2atan(⅓)) = e/16
e = (64/5) units.
f = (90-2atan(⅓)-2atan(⅕))°
tan(90-2atan(⅓)-2atan(⅕)) = g/(48/5)
g = (198/35) units.
Therefore;
Area Blue exactly in square units is;
½*(48/5)(198/35)
= 4752/175 square units.
